Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
16.1-b3
16.1-b
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
16.1
\( 2^{4} \)
\( - 2^{13} \)
$6.65950$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.1.1
$1$
\( 2 \cdot 7 \)
$1$
$1106.221345$
1.499429526
\( \frac{620979}{128} a^{3} - \frac{68657}{128} a^{2} - \frac{1152721}{64} a - \frac{1119033}{128} \)
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 3 a^{3} - 3 a^{2} - 10 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(3a^{3}-3a^{2}-10a+3\right){x}-a^{3}+a^{2}+3a-1$
128.2-a1
128.2-a
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
128.2
\( 2^{7} \)
\( - 2^{25} \)
$8.63630$
$(-a), (a^3-a^2-4a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.1
$1$
\( 2^{3} \)
$0.054835641$
$291.3963465$
2.425766985
\( \frac{620979}{128} a^{3} - \frac{68657}{128} a^{2} - \frac{1152721}{64} a - \frac{1119033}{128} \)
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( -a^{3} + 3 a^{2} - 2 a + 1\) , \( 0\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-a^{3}+3a^{2}-2a+1\right){x}$
512.3-d2
512.3-d
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{31} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.1
$1$
\( 2^{2} \)
$1$
$93.71397971$
1.778346732
\( \frac{620979}{128} a^{3} - \frac{68657}{128} a^{2} - \frac{1152721}{64} a - \frac{1119033}{128} \)
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( 0\) , \( -4 a^{3} + 10 a^{2} - 4\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+a-2\right){x}^{2}+\left(-4a^{3}+10a^{2}-4\right){x}$
512.3-g1
512.3-g
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{31} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.1
$1$
\( 2^{2} \)
$1$
$84.90356550$
1.611157468
\( \frac{620979}{128} a^{3} - \frac{68657}{128} a^{2} - \frac{1152721}{64} a - \frac{1119033}{128} \)
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a\) , \( -a^{3} - 7 a^{2} - 4 a + 8\) , \( -10 a^{3} - 10 a^{2} + 10 a + 3\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-a^{3}-7a^{2}-4a+8\right){x}-10a^{3}-10a^{2}+10a+3$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.